How to rotate a line?

This should answer your question. This code does what you want and shows you what happens depending on your choice of centre point of rotation. (Look up rotation matrices and direction cosine matrices for more information). This is an example for 3D rotation for 2D in the plane you could simplify and only use the Rz part.

Kevin

%%

clear all; close all; clc;

%Example coordinates
y=[2 4 6 8 10];
x=ones(size(y));

%Vertices matrix
V=[x(:) y(:) zeros(size(y(:)))];
V_centre=mean(V,1); %Centre, of line
Vc=V-ones(size(V,1),1)*V_centre; %Centering coordinates

a=30; %Angle in degrees
a_rad=((a*pi)./180); %Angle in radians
E=[0  0 a_rad]; %Euler angles for X,Y,Z-axis rotations

%Direction Cosines (rotation matrix) construction
Rx=[1        0        0;...
    0        cos(E(1))  -sin(E(1));...
    0        sin(E(1))  cos(E(1))]; %X-Axis rotation

Ry=[cos(E(2))  0        sin(E(2));...
    0        1        0;...
    -sin(E(2)) 0        cos(E(2))]; %Y-axis rotation

Rz=[cos(E(3))  -sin(E(3)) 0;...
    sin(E(3))  cos(E(3))  0;...
    0        0        1]; %Z-axis rotation

R=Rx*Ry*Rz; %Rotation matrix

Vrc=[R*Vc']'; %Rotating centred coordinates
Vruc=[R*V']'; %Rotating un-centred coordinates
Vr=Vrc+ones(size(V,1),1)*V_centre; %Shifting back to original location

figure;
plot3(V(:,1),V(:,2),V(:,3),'k.-','MarkerSize',25);  hold on; %Original
plot3(Vr(:,1),Vr(:,2),Vr(:,3),'r.-','MarkerSize',25); %Rotated around centre of line
plot3(Vruc(:,1),Vruc(:,2),Vruc(:,3),'b.-','MarkerSize',25); %Rotated around origin
axis equal; view(3); axis tight; grid on;